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Representations of fundamental groups of surfaces

Part of the Lecture Notes in Mathematics book series (LNM,volume 1167)

Keywords

  • Fundamental Group
  • Symplectic Structure
  • Tangent Cone
  • Mapping Class Group
  • Fuchsian Group

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References

  1. Arms, J., Marsden, J., and Moncrief, V., Symmetry and bifurcations of momentum mappings, Commun. Math. Phys. 78 (1981), 455–478.

    CrossRef  MathSciNet  MATH  Google Scholar 

  2. Atiyah, M. F., and Bott, R., The Yang-Mills equations on a compact Riemann surface, Phil. Trans. R. Soc. Lond. A 308 (1982), 523–615.

    CrossRef  MathSciNet  MATH  Google Scholar 

  3. Brown, K., Cohomology of groups, Graduate Texts in Mathematics 87, Springer-Verlag, New York 1982.

    MATH  Google Scholar 

  4. Culler, M., and Shalen, P. B., Varieties of group representations and splittings of 3-manifolds, Ann. of Math. 117 (1983), 109–146.

    CrossRef  MathSciNet  MATH  Google Scholar 

  5. Donaldson, S., A new proof of a theorem of Narasimhan and Seshadri, J. Diff. Geo. 18 (1983), 269–278.

    MathSciNet  MATH  Google Scholar 

  6. Goldman, W. M., Discontinuous groups and the Euler class, Doctoral Dissertation, University of California, Berkeley, 1980.

    Google Scholar 

  7. Goldman, W. M., Flat bundles with solvable holonomy II: Obstruction theory, Proc. A.M.S. 83 (1981), 175–178.

    CrossRef  MathSciNet  MATH  Google Scholar 

  8. Goldman, W. M., Characteristic classes and representations of discrete subgroups of Lie groups, Bull. A.M.S. (New Series) 6 (1982), 91–94.

    CrossRef  MathSciNet  MATH  Google Scholar 

  9. Goldman, W. M., The symplectic nature of fundamental groups of surfaces, Adv. in Math. (to appear).

    Google Scholar 

  10. Goldman, W. M., Invariant functions on Lie groups and Hamiltonian flows of surface group representations, (submitted).

    Google Scholar 

  11. Goldman, W. M., Topological components of spaces of representations of surface groups (in preparation).

    Google Scholar 

  12. Gunning, R. C., Lectures on vector bundles over Riemann surfaces, Princeton University Press, 1967.

    Google Scholar 

  13. Jankins, M., The space of homomorphisms of a Fuchsian group into PSL(2,ℝ), Doctoral Dissertation, University of Maryland, 1983.

    Google Scholar 

  14. Jankins, M., and Neumann, W., Homomorphisms of Fuchsian groups to PSL(2,ℝ), to appear).

    Google Scholar 

  15. Johnson, D. and Millson, J., Deformation spaces of compact hyperbolic manifolds, (to appear in Discrete groups in geometry and analysis, Proceedings of a conference held at Yale University in honor of G, D, Mostow on his sixtieth birthday, March 1984).

    Google Scholar 

  16. Lusztig, G., Novikov's higher signature and families of elliptic operators, J. Diff. Geo. 7 (1972), 229–256.

    MathSciNet  MATH  Google Scholar 

  17. Magnus, W., Rings of Fricke characters and automorphism groups of free groups, Math. Zeit. 170 (1980), 91–103.

    CrossRef  MathSciNet  MATH  Google Scholar 

  18. Meyer, W., Die signatur von lokalen koeffiziensystemen und faserbudeln, Bonner Math. Schriften 53 (1972).

    Google Scholar 

  19. Milnor, J. W., On the existence of a connection with curvature zero, Comm. Math. Helv. 32 (1957), 2 [16]-223.

    Google Scholar 

  20. Morgan, J., and Shalen, P. B., Valuations, trees, and degenerations of hyperbolic structures I (to appear).

    Google Scholar 

  21. Narasimhan, M. S. and Seshadri, C. S., Stable and unitary vector bundles on a compact Riemann surface, Ann. of Math. 82 (1965), 540–567.

    CrossRef  MathSciNet  MATH  Google Scholar 

  22. Newstead, P. E., Characteristic classes of stable bundles over an algebraic curve, Trans. A.M.S. 169 (1972), 337–345.

    MathSciNet  MATH  Google Scholar 

  23. Nijenhuis, A. and Richardson, R. W., Deformations of homomorphisms of Lie groups and Lie algebras, Bull. A.M.S. 73 (1967), 175–179.

    CrossRef  MathSciNet  MATH  Google Scholar 

  24. Raghunathan, M. S., Discrete Subgroups of Lie groups, Erg. der Math. Bd. 68, Springer-Verlag (1972).

    Google Scholar 

  25. Toledo, D., Harmonic maps from surfaces to certain Kahler manifolds, Math. Scand. 45 (1979), 13–26.

    MathSciNet  MATH  Google Scholar 

  26. Toledo, D., On the Schwarz lemma for harmonic maps and characteristic classes of flat bundles, (preprint).

    Google Scholar 

  27. Weil, A., Remarks on the cohomology of groups, Ann. of Math. 80 (1964), 149–157.

    CrossRef  MathSciNet  MATH  Google Scholar 

  28. Whitney, H., Elementary properties of real algebraic varieties, Ann. of Math. 66 (1957), 545–556.

    CrossRef  MathSciNet  MATH  Google Scholar 

  29. Wolpert, S., On the symplectic geometry of deformations of a hyperbolic surface, Ann. of Math. 117 (1983), 207–234.

    CrossRef  MathSciNet  MATH  Google Scholar 

  30. Wood, J. W., Bundles with totally disconnected structure group, Comm. Math. Helv. 51 (1976), 183–199.

    Google Scholar 

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© 1985 Springer-Verlag

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Goldman, W.M. (1985). Representations of fundamental groups of surfaces. In: Geometry and Topology. Lecture Notes in Mathematics, vol 1167. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0075218

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  • DOI: https://doi.org/10.1007/BFb0075218

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-16053-3

  • Online ISBN: 978-3-540-39738-0

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